Law of Variable Proportion: Detailed Explanation

Imagine you are standing at your favourite ice cream parlour and eagerly waiting to gobble it up, and you start eating the scoops one after the other continuously. At first, your satisfaction level is at its highest peak and after having 3 or 4 scoops, your level is still increasing, but now at a diminishing rate. Eventually, a point will come when you will be almost close to being satisfied and full, and there will be fewer chances for you to eat another scoop. This is exactly what the law of variable proportion means. Being one of the most popular concepts in the field of business economics and managerial economics, here is an insightful blog to help you understand every aspect of the law.

What is the Law of Variable Proportions?

The Law of Variable Proportions states that as the quantity of a factor is increased while keeping other factors constant, the Total Product (TP) first rises at an incremental rate, then at a decremental rate, and lastly, the total production begins to fall. In other words, as one of the factors in production makes some variation in its quantity, keeping all the other factors constant, the ratio between all the factors starts varying, which further influences the level of output.

For example, if a farmer keeps adding more labourers to a small piece of land, the output will go up at first. However, after a certain point, adding more workers becomes less effective and might even lower overall productivity. This happens because the fixed resources, like land and tools, become inadequate for all the workers to use effectively. The law shows that beyond a certain limit, increasing one input results in diminishing or even negative returns instead of more output.

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Assumptions of the Law of Variable Proportions

The law of variable proportion works under the following situations or conditions that must be met for it to apply. These conditions are called assumptions. They help clarify how production changes when the amount of one input increases while all other inputs stay the same.

Constant State of Technology

The first assumption is that the state of technology given for the situation remains unchanged. In case, the technology gets improved, then the marginal product may rise rather than diminish.

Fixed Quantity of Other Inputs

This means that there should be some inputs or factors given in a certain situation which should remain fixed in terms of their quantity. By changing the factor proportions, we can understand the effects on the output. However, the law would not work if all the factors were altered in proportion.

Ability to Change Input Ratios

The third assumption is that the law can only work if there is scope for varying proportions of factors, as fixed proportions might not yield effective results.

Also Read: Class 11 Introduction to Statistics in Economics

Terms to Remember

Before we go ahead with a detailed explanation of the law, let us first understand the different terms that we will be using in this blog.

Production Function

As we know, production implies the transformation of physical inputs into physical outputs. Therefore, the production function explains the interrelationship between the factor inputs and outputs.

Total Product (TP)

Total Product (TP) is also known as total output, following varied values of a physical variable input along with a fixed amount of input. This process gives us the value of TP.

Average Product (AP)

Average Product equals the Total Product (TP) divided by the total number of variable inputs. In other words, AP is the output per unit.

Marginal Product (MP)

Marginal Product or output is derived when the producer employs additional units of inputs in variable factors, which further means that it is the rate at which the TP rises.

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What are the Stages of the Law of Variable Proportion?

In order to understand this in detail, let us take an example. Imagine you own a land wherein you produce rice by employing more and more labour (variable factors). The table given below explains the situation further:

In the above table and graph of the Law of Variable Proportions, you will notice that:

• With up to 3 units of labour employed, the TP is rising at an increasing rate (2,6,12). This constitutes Stage 1 of the law, which is the Stage of Increasing Returns. Therefore, during the first stage, the TP curve increases significantly.
• Beyond the 3rd unit of labour, the TP starts rising at a diminishing rate (12,16,18), which means the TP curve rises at a slower rate. This eventually makes the marginal product (MP) start to fall. Constituting the second stage of the Law of Variable Proportion which is called the Stage of Diminishing Returns.
• After the employment of 6 units of labour, the TP starts to fall, indicating the 3rd stage which is the Stage of Negative Returns. Even after employing 6 units of labour, it fails to yield the marginal product, that is when the MP comes to zero. Eventually, the TP curve starts sloping down and the marginal product goes negative on the x-axis.

Relation Between TP, MP and AP in the Law of Variable Proportion

Now that we understand how Total Product (TP), Marginal Product (MP), and Average Product (AP) behave across the three stages of the Law of Variable Proportion, let us explore how these three are interconnected. Their relationship is essential to understanding how output responds to changes in the variable input and how efficiency varies at different stages of production.

1. When TP increases at an increasing rate, the MP and AP also increase. However, at this stage, MP>AP
2. When TP increases at a decreasing rate, the MP and AP start to fall. When MP starts falling significantly and AP falls at a low rate, it means that now MP<AP.
3. When TP falls, MP goes negative, and AP falls consistently, remaining above the x-axis.
4. MP intersects AP when the latter is at the maximum, this is where MP=AP.

Now arises a Million Dollar Question: Which stage of the Law of Variable Proportion should a firm operate in? Is it Stage 1, 2 or 3? Let’s give you a simple answer to this question.

As a rational firm, the optimal utilisation of both the fixed and variable inputs would take place only in Stage 2 of the Law of Variable Proportion. That is the only time when all the inputs are used economically. Additionally, the MP and AP of both the inputs are positive yet diminishing. Whereas, if a firm operates in the first stage, the marginal product of the fixed input (land) is still in a negative form. This is because the lesser units of labour are using the land in a large proportion, thereby yielding no marginal product.

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Additional Reads

Nature and Scope of Economics	Class 11 Introduction To Microeconomics
Class 11 Introduction to Statistics in Economics	Development Economics
PhD in Economics in Europe	Economics Project for Class 12

You must be surprised to know that the Law of Variable Proportion has universal applicability in any branch of production. Forming the basis of several doctrines in Economics, students can understand its role in the study of the Theory of Production. So, if you’re looking forward to building a career in Economics and need assistance in choosing the right university abroad, talk to us at Leverage Edu.